Math question :a ladder leans against a building forming an angle of 56 degrees with the ground.The base of the ladder is 3 feet from the building. Use the cosine to determine the length of the ladder.
To find the length of the ladder, we can use the cosine function. The cosine of an angle is equal to the adjacent side divided by the hypotenuse.
In this case, the adjacent side is the distance from the building to the base of the ladder, which is given as 3 feet. The hypotenuse is the length of the ladder that we are trying to find.
Using the cosine function, we can write the equation:
cos(56°) = adjacent side / hypotenuse
Let's solve for the hypotenuse:
cos(56°) = 3 / hypotenuse
To isolate the hypotenuse, we can rearrange the equation:
hypotenuse = 3 / cos(56°)
Now, we can use a calculator to find the value of cos(56°). Once we have that value, we can substitute it back into the equation and calculate the length of the ladder.
To find the length of the ladder, we can use the cosine function. The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. In this case, the ladder is the hypotenuse, and the adjacent side is the base of the ladder.
Let's denote the length of the ladder as "L". The angle of 56 degrees forms a right triangle with the base of 3 feet and the ladder as the hypotenuse. Using the cosine function:
cos(56 degrees) = adjacent / hypotenuse
cos(56 degrees) = 3 / L
To find the length of the ladder, we need to isolate "L" by multiplying both sides of the equation by "L":
L * cos(56 degrees) = 3
Now, we can divide both sides of the equation by cos(56 degrees) to solve for "L":
L = 3 / cos(56 degrees)
Using a calculator, evaluate cos(56 degrees) to determine the value. Then, divide 3 by that value to find the length of the ladder.
Did you draw a diagram? Review the cosine function?
3/x = cos56°